[CAG19] — Free choice disjunction as a rational speech act #

RSA model of [CAG19] (SALT 29): free choice ("You may take an apple or a pear" ⤳ "You may take an apple") emerges from RSA once semantic uncertainty ([BLG16]) is added: agents reason over two interpretation functions — ℐ₁ (classical modal logic) and ℐ₂ (strengthened via [Fox07]-style exhaustification) — so a bare disjunct risks the "Only A" reading; the disjunction avoids that risk and the listener inverts the avoidance. States and utterances extend [Fra11]'s IBR model; the recursion is [FG12]'s, with P_L0(w|u,ℐ) ∝ ℐ(u,w)·P(w), P_S1(u|w,ℐ) ∝ [P_L0]^α, and P_L1(w|u) ∝ P(w)·Σ_ℐ P_S1(u|w,ℐ).

Instantiated on the canonical pipeline: the speaker is RSA.Canonical.S1 at the natural-exponent informativity utility (RSA.Canonical.powUtility with α = 2, i.e. rsaUtility at zero cost), the listener RSA.Canonical.L1 (the joint posterior over FCState × Interp). Findings are posterior-mass comparisons closed by dominance bounds on softmax weights — no numeric reflection. Since the FCI/EI events constrain only the world coordinate and the interpretation prior is uniform, joint-posterior event masses coincide with the paper's ℐ-marginalised L1. The paper's tables use α = 100; at the α = 2 used here the paper notes L1 assigns "only 70%" to the FCI states given Or (our exact masses give ≈ 70.2%).

Main statements #

fci_derived — given Or, L1 favours the FCI states (Only One, Any Number) under a uniform prior; ei_uniform — at α = 2 the EI states also carry more mass (a low-α observation of ours: at the paper's α = 100 the EI split is exactly ½/½, and the paper derives EI from priors only).
ei_defeated_by_prior — with the paper's 75%-Any-Number prior the EI comparison reverses: EI tracks world knowledge.
speaker_or_onlyOne_exh / speaker_prefers_a_at_onlyA_exh — the avoidance mechanism at S1.

Implementation notes #

The paper's FCI-robustness claim (75% prior on Only A leaves FCI intact at α = 100) is parameter-dependent: at α = 2 it reverses (the non-FCI score sum ≈ 0.32 dominates ≈ 0.065 — the low-α speaker does not reliably avoid Or at Only A, and the 12× prior swamps the avoidance; at α = 100 the Only-A terms decay like (15/16)^α). The reversal qualifies the paper's generally-worded robustness conclusion, which is stated without an α-caveat. Per the library's policy on findings whose truth depends on an exact parameter value, it is recorded as prose, not as a theorem. The paper's Table-8 null-utterance robustness check is recorded as prose for space (its α = 2 values are documented in the final section), and the §4 negation model is not formalised.

[CAG19] — Free choice disjunction as a rational speech act #

Main statements #

Implementation notes #

States, utterances, interpretation functions (Table 2, (5), (6), (7)) #

ENNReal budget helpers #

The FCI / EI events #

The basic model, uniform prior #

Prior sensitivity: the asymmetric-prior model #

Without the conjunctive alternative (prose) #